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"Economic theory predicts that you are not enjoying this book as much as you thought you would", remarks Steven E. Landsburg at the start of one of the most enjoyable chapters of The Armchair Economist. The point turns out to be this: the fact that you have chosen to read it is a sign that you have probably overvalued it in relation to all the other books you could have read instead.

First the executive summary: read these excellent books, and make sure all your friends and relations and bright pupils (if you are a teacher) or teachers (if a bright pupil) do so too. Mathematical Vistas (MV) is the sequel to the same authors' earlier Mathematical Reflections (MR). Each book is a series of explorations of mathematical topics, informed by a definite idea of what mathematics is, and how it should be taught.

If you watch a steam engine, you may not know how it works but you can soon get a fairly good idea of its behaviour, and you can predict its future behaviour accurately. Even though you don't understand its workings, you can see it's a pretty simple machine, so you can trust it to behave in a simple way: you have confidence in your predictions based on a short sample of its behaviour.

ver the last hundred years, human understanding of the nature of the universe has expanded at a mind-boggling rate; and over the last forty, Kip Thorne, along with Stephen Hawking, who wrote the foreword to this book, have been among the group of people shining most light into the darkness. But, aware that his research is carried out on behalf of us all, Thorne has not neglected the task of explaining its results to the rest of us.

What is the nature of the universe that we live in? This is a question that has exercised philosophers and scientists for as long as people have been able to think. Almost everyone has asked it at one time or another, in one form or another. It is hard to imagine a more fundamental question.